I would like to have a custom post type which has 'Activate' and 'Deactivate' rather than 'Publish' and 'Move to Trash'. Once a post is deactivated, the user can go and delete it permanently.

This functionality is required due to the nature of the custom post type. Is it possible to disable the emptying of trash (by default 30 days) for this particular custom post type, so that the 'deactivated' posts will remain there and not be cleaned up?

Yes this can also work, but adds an extra layer on top of the WordPress Published/Draft system, which I was hoping I could repurpose into Activated/Deactivated, exactly the way plugins work in WordPress.
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drtanzAug 20 '12 at 13:17

Ok, I have no idea if you can hook into that functionality. I added a little more info about the trash situation to my answer above
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woonyAug 21 '12 at 7:05

Removing scheduled delete would be nice, but I need to know if we can specify the deletion of that particular post type, rather than all deletions.
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drtanzAug 21 '12 at 10:45

I do not think that will be possible. Your easiest solution remains my first suggestion I think.
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woonyAug 21 '12 at 12:35